Spatiotemporal correlations of aftershock sequences

Aftershock sequences are of particular interest in seismic research since they may condition seismic activity in a given region over long time spans. While they are typically identified with periods of enhanced seismic activity after a large earthquake as characterized by the Omori law, our knowledge of the spatiotemporal correlations between events in an aftershock sequence is limited. Here, we study the spatiotemporal correlations of two aftershock sequences form California (Parkfield and Hector Mine) using the recently introduced concept of "recurrent" events. We find that both sequences have very similar properties and that most of them are captured by the space-time epidemic-type aftershock sequence (ETAS) model if one takes into account catalog incompleteness. However, the stochastic model does not capture the spatiotemporal correlations leading to the observed structure of seismicity on small spatial scales.Comment: 31 pages, 5 figure

Strong-field dynamics in small molecules

Abweichender Titel laut Übersetzung der Verfasserin/des VerfassersZsfassung in dt. SpracheChemische Reaktionen und molekulare Dynamik effizient zu kontrollieren und zu steuern ist nicht nur ein großes Ziel in der Grundlagenforschung, sondern auch von großem industriellen Interesse. Starke, ultrakurze Laserpulse mit Intensitäten um 1014 W/cm2 und Pulslängen, die nur wenige Schwingungsperioden umfassen, erlauben die Bewegung von Elektronen und Kernen auf einer Femtosekunden-Skala und sogar darunter zu kontrollieren. Die Analyse und Interpretation von Experimenten, die diese Möglichkeit belegen, erfordert jedoch Modellbildungen, die nur auf theoretischen Ansätzen beruhen können. Ziel dieser Arbeit ist die Analyse von drei jüngst durchgeführten Experimenten. Fokus der Experimente war die Kontrolle sowohl der nuklearen als auch der elektronischen Dynamik in kleinen Molekülen. Die vorliegende theoretische Arbeit gibt einen Einblick in die zugrundeliegenden Prozesse und erlaubt es die relevanten Prozesse, die die Dynamik grundlegend steuern, zu identifizieren und zu verstehen. Um das zu erreichen werden verschiedene Ansätze aus der Physik und der Chemie angewandt und vereint. Die Arbeit ist in drei Teilen strukturiert: Der erste Teil befasst sich mit der Starkfeld-Ionisation von H+ 2 . Die folgenden zwei Teile beschäftigen sich mit der Analyse von Experimenten zur Kontrolle von chemischen Reaktionen, namentlich mit der Kontrolle der Fragmentierung von C2H2 mittels der "carrier-envelope" Phase von ultrakurzen Pulsen und mittels der relativen Ausrichtung zwischen Molekül und Polarisationsachse. Ziel des ersten Teiles der Arbeit ist es, Resultate von experimentell gemessenen Photoelektronspektren von H+2 in zirkular polarisierten Feldern zu interpretieren. Der Fokus liegt dabei auf der Analyse der experimentell beobachteten Rotation des winkelaufgelösten Photoelectronspektrums relativ zu Vorhersagen, die auf Starkfeld-Näherungen beruhen. Zu diesem Zweck wurde ein semi-klassisches Modell entwickelt. Die vorliegenden Resultate zeigen, dass klassische Trajektorien Monte Carlo Rechnungen viele experimentelle Resultate korrekt widerspiegeln. In Folge dessen erlauben die semi-klassischen Rechnungen eine einfache und intuitive Interpretation von verschiedenen Einflussfaktoren, wie dem anisotropen Coulomb Potential des Ions und dem komplexen zeitlichen Verhalten der Ionisation. Dadurch ermöglichen die Rechnungen beispielsweise eine Interpretation der auf den ersten Blick widersinnig erscheinenden sehr schwachen Intensitätsabhängigkeit des Photoelektronspektrums: Laut der semi-klassischen Analyse resultiert diese aus zwei konkurrierenden Prozessen mit gegensinniger Intensitätsabhängigkeit. Weitere Effekte illustrieren den Einfluss des Startimpulses der Trajektorien. Multiple-Ionisationsereignisse pro Laserperiode spielen laut dem semi-klassischen Modell jedoch keine wesentliche Rolle für die resultierende Winkelabhängigkeit des Photoelektronspektrum. Der zweite Teil der Arbeit beschäftigt sich mit größeren Molekülen. Die Experimente zur Zerfallskontrolle von C2H2 durch gezielte Kontrolle der "carrier-envelope" Phase werden anhand von quantenchemischen Rechnungen, Quantendynamik-Simulationen und semiklassischen Modellen interpretiert. Als grundlegender Regelungsmechanismus wurde ein Energie-Schwellenwert-Effekt in der Doppelionisation via Elektronen-Rekollision identifiziert. Andere Einflüsse, so wie die "carrier-envelope" Phasenabhängigkeit von Feldanregungen, sind zwar vorhanden, dürften aber eine untergeordnete Rolle spielen. Der neu entdeckte Energie-Schwellenwert-Effekt könnte eine Fragmentierungskontrolle in einer ganzen Reihe von Molekülen erlauben. Der dritte Teil der Arbeit beschäftigt sich mit der Kontrolle des Zerfalls von C2H2 mittels der relativen Ausrichtung der Laserpolarisationsachse zur Molekülachse. Mittels eines Modells, das die sequentielle Ionisation beschreibt, konnte sowohl qualitative als auch quantitative Übereinstimmung mit den experimentellen Daten für mehrere Zerfallskanäle erzielt werden. Das Modell basiert auf TD-DFT Rechnungen und einem effektiven Einteilchenmodell zur Tunnel-Ionisation. Obwohl diese beiden Methoden auf unterschiedlichen Näherungen beruhen, sind die so erzielten Ergebnisse konsistent. Für einige Zerfallskanäle konnte gezeigt werden, dass Elektronenstoßionisation nach Elektronenrückstreuung des primären Elektrons eine wesentliche Rolle spielt. In diesem Zusammenhang konnte anhand von vereinfachten differenziellen Wirkungsquerschnitten gezeigt werden, dass der Stoßprozess selber einen nicht zu vernachlässigenden Einfluss auf die Winkelabhängigkeit von Elektronen-Rückstoß-Ionisation haben könnte. Dieser Stoßprozess wird üblicherweise in der Analyse der Winkelabhängigkeit von Elektronen-Rückstoß-Ionisation vernachlässigt. Die vorliegenden Rechnungen legen jedoch nahe, dass die Winkelabhängigkeit der Stoßquerschnitte in eine Gesamtanalyse des Prozesses eingehen sollte. Dagegen konnte gezeigt werden, dass die Winkelabhängigkeit von Dipolanregungen zwar stark ist, jedoch aufgrund ihrer relativ kleinen Wahrscheinlichkeit bei den verwendeten Intensitäten keine wesentliche Rolle in der Kontrolle des molekularen Zerfalls spielt.Steering and guiding molecular reactions and molecular dynamics is a long standing goal in chemistry and physics. Strong and ultrashort infrared pulses with intensities around 1014 W/cm2 and pulse lengths of less than 5 fs, corresponding to 1-2 optical cycles, allow influencing the electronic and nuclear motion on femtosecond and even sub-femtosecond timescales. In order to analyse and interpret experimental results, detailed theoretical investigations are necessary. This work focusses on three recent experiments, one addressing the electronic dynamics in molecules subject to intense fields and two addressing the strong field control of nuclear dynamics. This work provides an analysis of the processes involved in order to identify the relevant physical mechanisms governing the dynamics. This is achieved by applying a large variety of different approaches from physics and chemistry. More precisely, the first part of this thesis deals with the strong field ionization of H+2 in circularly polarized fields and the resulting photoelectron spectrum, which is studied within a semi-classical model. The focus is to provide an analysis and interpretation of the observed rotation of the photoelectron momentum distribution compared to predictions from the strong-field approximation (SFA). The work shows that classical trajectory Monte Carlo calculations can reproduce and explain many experimentally observed features in the molecular strong-field ionization of H+2 : the classical trajectory calculations thus provide a simple approach to testing the influence of the Coulomb potential and multiple ionization bursts. For instance, the model allows interpreting the counterintuitive intensity independence of the angular photoelectron spectrum as a result of two rivalling processes: the intensity dependence of the tunnel exit and the field interaction in the continuum. The model also illustrates the importance of the initial momentum distribution assigned to the trajectories on the momentum and angle resolved photoelectron spectrum and the rotation thereof. Multiple ionization bursts are found not to be responsible for the observed rotation of the photoelectron spectrum compared to SFA predictions. The second and third part of the thesis deal with the interpretation of experiments investigating the possibility to control fragmentation reactions of C2H2 using strong few-cycle laser pulses: The second part deals with the reaction control of C2H2 using the carrier-envelope phase of few-cycle infra-red laser fields as control tool. The combined analysis of quantum chemical calculations, quantum dynamical calculations, and a semi-classical model for recollisional ionization allows identifying an energy threshold effect in recollisional ionization as the main control mechanism. Other influences, such as field excitations, are found to be of minor importance. The novel control mechanism discovered in the course of this work is likely to allow fragmentation control for a large number of small molecules. In the third part of the thesis, the reaction control of C2H2 via molecular alignment is investigated. A study of the alignment dependence of sequential ionization allows the qualitative and quantitative reproduction of several experimentally observed features. The alignment dependence of sequential ionization is thereby studied using both, a TDDFT approach and a tunnel-ionization approach based on the Dyson orbital formalism. Although the two methods depend on different approximations and simplifications, the results are found to be consistent. For some fragmentation channels, recollisional ionization is found to play an important role. It is shown that the electron impact process, which is often neglected in models, may have a significant influence on the alignment dependence of recollisional ionization. This is illustrated by calculating singly-differential electron-impact ionization cross-sections within several different approximations. Field driven dipole transitions, which show a strong alignment dependence, have only little influence on the resulting fragmentation yield at the experimentally relevant intensities due to the small transition probabilities.16

Quantum Monte Carlo Calculations on a Benchmark Molecule–Metal Surface Reaction: H 2 + Cu(111)

International audienceAccurate modeling of heterogeneous catalysis requires the availability of highly accurate potential energy surfaces. Within density functional theory, these can -unfortunately- depend heavily on the exchange-correlation functional. High-level ab initio calculations, on the other hand, are challenging due to the system size and the metallic character of the metal slab. Here, we present a quantum Monte Carlo (QMC) study for the benchmark system H 2 + Cu(111), focusing on the dissociative chemisorption barrier height. These computationally extremely challenging ab initio calculations agree to within 1.6 ± 1.0 kcal/mol with a chemically accurate semiempirical value. Remaining errors, such as time-step errors and locality errors, are analyzed in detail in order to assess the reliability of the results. The benchmark studies presented here are at the cutting edge of what is computationally feasible at the present time. Illustrating not only the achievable accuracy but also the challenges arising within QMC in such a calculation, our study presents a clear picture of where we stand at the moment and which approaches might allow for even more accurate results in the future

Time-Resolved Local pH Measurements during CO2_2 Reduction Using Scanning Electrochemical Microscopy: Buffering and Tip Effects

The electrochemical reduction of CO$_2$ is widely studied as a sustainable alternative for the production of fuels and chemicals. The electrolyte’s bulk pH and composition play an important role in the reaction activity and selectivity and can affect the extent of the buildup of pH gradients between the electrode surface and the bulk of the electrolyte. Quantifying the local pH and how it is affected by the solution species is desirable to gain a better understanding of the CO$_2$ reduction reaction. Local pH measurements can be realized using Scanning Electrochemical Microscopy (SECM); however, finding a pH probe that is stable and selective under CO$_2$ reduction reaction conditions is challenging. Here, we have used our recently developed voltammetric pH sensor to perform pH measurements in the diffusion layer during CO$_2$ reduction using SECM, with high time resolution. Using a 4-hydroxylaminothiophenol (4-HATP)/4-nitrosothiophenol (4-NSTP) functionalized gold ultramicroelectrode, we compare the local pH developed above a gold substrate in an argon atmosphere, when only hydrogen evolution is taking place, to the pH developed in a CO$_2$ atmosphere. The pH is monitored at a fixed distance from the surface, and the sample potential is varied in time. In argon, we observe a gradual increase of pH, while a plateau region is present in CO$_2$ atmosphere due to the formation of HCO$_3$– buffering the reaction interface. By analyzing the diffusion layer dynamics once the sample reaction is turned “off”, we gain insightful information on the time scale of the homogeneous reactions happening in solution and on the time required for the diffusion layer to fully recover to the initial bulk concentration of species. In order to account for the effect of the presence of the SECM tip on the measured pH, we performed finite element method simulations of the fluid and reaction dynamics. The results show the significant localized diffusion hindrance caused by the tip, so that in its absence, the pH values are more acidic than when the tip is present. Nonetheless, through the simulation, we can account for this effect and estimate the real local pH values across the diffusion layer

Diffusion Monte Carlo for Accurate Dissociation Energies of 3d Transition Metal Containing Molecules

Transition metals and transition metal compounds are important to catalysis, photochemistry, and many superconducting systems. We study the performance of diffusion Monte Carlo (DMC) applied to transition metal containing dimers (TMCDs) using single-determinant Slater–Jastrow trial wavefunctions and investigate the possible influence of the locality and pseudopotential errors. We find that the locality approximation can introduce nonsystematic errors of up to several tens of kilocalories per mole in the absolute energy of Cu and CuH if Ar or Mg core pseudopotentials (PPs) are used for the 3d transition metal atoms. Even for energy differences such as binding energies, errors due to the locality approximation can be problematic if chemical accuracy is sought. The use of the Ne core PPs developed by Burkatzki et al. (<i>J. Chem. Phys.</i> <b>2008</b>, <i>129</i>, 164115), the use of linear energy minimization rather than unreweighted variance minimization for the optimization of the Jastrow function, and the use of large Jastrow parametrizations reduce the locality errors. In the second section of this article, we study the general performance of DMC for 3d TMCDs using a database of binding energies of 20 TMCDs, for which comparatively accurate experimental data is available. Comparing our DMC results to these data for our results that compare best with experiment, we find a mean unsigned error (MUE) of 4.5 kcal/mol. This compares well with the achievable accuracy in CCSDT(2)_Q (MUE = 4.6 kcal/mol) and the best all-electron DFT results (MUE = 4.5 kcal/mol) for the same set of systems (Truhlar et al. <i>J. Chem. Theory Comput.</i> <b>2015</b>, <i>11</i>, 2036–2052). The mean errors in DMC depend less on the exchange-correlation functionals used to generate the trial wavefunction than the corresponding mean errors in the underlying DFT calculations. Furthermore, the QMC results obtained for each molecule individually vary less with the functionals used. These observations are relevant for systems such as molecules interacting with transition metal surfaces where the DFT functionals performing best for molecules (hybrids) do not yield improvements in DFT. Overall, the results presented in this article yield important guidelines for both the assessment of the achievable accuracy with DMC and the design of DMC calculations for systems including transition metal atoms

Attosecond-Recollision-Controlled Selective Fragmentation of Polyatomic Molecules

Control over various fragmentation reactions of a series of polyatomic molecules (acetylene, ethylene, 1,3-butadiene) by the optical waveform of intense few-cycle laser pulses is demonstrated experimentally. We show both experimentally and theoretically that the responsible mechanism is inelastic ionization from inner-valence molecular orbitals by recolliding electron wavepackets, whose recollision energy in few-cycle ionizing laser pulses strongly depends on the optical waveform. Our work demonstrates an efficient and selective way of pre-determining fragmentation and isomerization reactions in polyatomic molecules on sub-femtosecond time-scales